Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network

  Advanced Search  

Resource-Bounded Strong Dimension versus Resource-Bounded Category

Summary: Resource-Bounded Strong Dimension versus
Resource-Bounded Category
John M. Hitchcock a
and A. Pavan b,1
aDepartment of Computer Science, University of Wyoming,
bDepartment of Computer Science, Iowa State University,
Classically it is known that any set with packing dimension less than 1 is meager
in the sense of Baire category. We establish a resource-bounded extension: if a class
X has -strong dimension less than 1, then X is -meager. This has the applica-
tions of explaining some of Lutz's simultaneous -meager, -measure 0 results and
providing a new proof of a Gu's strong dimension result on infinitely-often classes.
Key words: computational complexity, resource-bounded category,
resource-bounded dimension, resource-bounded measure
1 Introduction
The most common mathematical notions of size and dimension now have
resource-bounded versions that are useful for complexity classes. We use to
denote a resource bound such as p (polynomial time) or pspace (polynomial


Source: Aduri, Pavan - Department of Computer Science, Iowa State University


Collections: Computer Technologies and Information Sciences